I found a great article in the Houston Herald from September 2011. Lots of nice photos, and these timeline clues:

It changed hands “several times over the years”.

Jaretta Lankford owned the drive-in and adjacent indoor theater “for most of the 90s.” The original screen blew down “in the mid-1990s” and was replaced with the screen that endures to at least 2011. That was also when it upgraded to FM sound, keeping a few car speakers too.

It was purchased in February 2010 from someone who “only had it less than a year”.

As of the article, Samantha Thomas owned the Phoenix and ran it with her parents, Richard and Hillary Thomas, and sister Noel.

There’s another great article, with a ton of very nice photos, in yesterday’s Houston Herald. Here are a few new details:

Long-time Texas County residents Josh and Jennifer Shelton took ownership of the business in June 2018. The Faith Fellowship youth group painted the projection / concession building on Day One.

The Phoenix “can accommodate close to 150 vehicles”. It still uses FM sound, and there was no reference to leftover speakers.

“The drive-in was open on weekends during the holiday season, and will operate on a week-by-week basis until re-opening for good in the spring and showing movies into late fall.” Since the indoor theater operates pretty much all year, the drive-in appears to run whenever weather permits.

The 1951-52 MPA listed the Sunset without further details. The 1952-55 editions had the capacity of 150, “Owner or Booker” was H. E. Lay. The 1956-66 Almanacs listed R. D. Fischer as owner/booker. The MPAs stopped listing owners for a decade, then the 1977 edition listed the Sunset with a capacity of 200, owner Wyatt. That’s how it stayed through the final drive-in list, the 1988 Almanac.